Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Triangle ABC is right angle at A. The points P and Q are on hypotenuse BC such that BP = PQ = QC. If AP = 3 and AQ = 4, then length BC is equal to
A
B
C
D
7
Text Solution
Verified by ExpertsThe correct answer is:
A
Let BP = PQ = QC = x
In Δ ABP, using cosine rule
9 = c 2 + x 2 – 2cx cosB
But cosB = 
........(1)
⇒ 9 = x 2 + 
similarly using cosine rule in Δ ACQ , we get
16 = x 2 + 
.......(2)
Adding (1) and (2), we get 25 = 2x 2 + 
∴ 25 = 2x 2 + 
∴ 25 = 2x 2 + 3x 2
∴ x 2 = 5
∴ BC = 3x = 
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
In a Δ ABC, prove that :
(i)a sin (B – C) + b sin (C – A) + c sin (A – B) = 0
(ii) + + = 0
(iii)…
Find the real value of x such that x 2 + 2x, 2x + 3 and x 2 + 3x + 8 are lengths of the sides of a …
The angles of a Δ ABC are in A.P. (order being A, B, C) and it is being given that b : c = : , th…
If cos A + cos B = 4 sin 2 , prove that sides a, c, b of the triangle ABC are in A.P.
If in a Δ ABC, = , then prove that a 2 , b 2 , c 2 are in A.P.
In a triangle ABC, prove that for any angle θ , b cos (A − θ ) + a cos (B + θ ) = c cos θ .